So that proves if det(-A)=0, then det(adj A)=0? and it is indeed true? I am confused about how exactly the adjoint relates to the original matrix, let alone the negative matrix. The adjoint is the transpose of the coefficient matrix, but I am not entirely clear on how to get the coefficient matrix. Would your statement (. Since . If the adjoint was invertible then it would force which is a contradiction. Thus, adjoint is not invertible and so its determinant must be zero.) be a sufficient proof? I am creating an example to go with it. I'm just having a hard time knowing when enough information is given to be considered a proof. Thank you for all of your help!